Contents

An example for mathematical analysis is limits. Limits are used to see what happens very close to things. Limits can also be used to see what happens when things get very big. For example, is never zero, but as n gets bigger gets close to zero. The limit of as n gets bigger is zero. It is usually said "The limit of as n goes to infinity is zero". It is written as .

The counterpart would be . When the gets bigger, the limit goes to infinity. It is written as .

The function is a line. The shows the slope of the function and the shows the position of the function on the ordinate. With two points on the line, it is possible to calculate the slope with:

.

A function of the form , which is not linear, cannot be calculated like above. It is only possible to calculate the slope by using tangents and secants. The secant passes through two points and when the two points get closer, it turns into a tangent.

is read as "the integral of f, from a to b" and refers to the area between the x-axis, the graph of function f, and the lines x=a and x=b. The is the point where the area should start and the where the area ends.